Abstract.
In this work, for an exchangeable sequence of random variables {X i, i≥1}, and two nondecreasing sequences of positive integers {h n, n≥2} and {k n, n≥2}, where h n+k n≤n, ∀n≥2, we prove that {R n,hn,kn/n, n≥2} forms a reverse submartingale sequence, where , and X 1,n≤X 2,n≤…≤X n,n are the order statistics based on {X 1,…,X n}.
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Received: December 1998
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Huang, WJ., Su, JC. Reverse submartingale property arising from exchangeable random variables. Metrika 49, 257–262 (1999). https://doi.org/10.1007/PL00020901
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DOI: https://doi.org/10.1007/PL00020901